Math 522: Topics in Analysis
In this course we will discuss general links between quantum spectra and quantum dynamics. That is, we will study the time evolution given by the Schrödinger equation, either for a general self-adjoint operator or specifically for a Schrödinger operator, and establish relationships between the long-time behavior of the solution and the spectral measure associated with the initial state. Topics to be covered include the spectral theorem, various ways to capture wavepacket spreading, the RAGE Theorem, dynamics for uniformly Hölder continuous measures, dynamical bounds in terms of various dimensions of spectral measures, and dynamics for pure point measures along with the problem of proving dynamical localization.
Prerequisites: Previous exposure to measure theory and some basic functional analysis will be assumed.
Meeting Time: TR 9:25 AM -- 10:40 AM
Location: Herman Brown (Room 453)
Email: [my last name] at rice dot edu
Office: Herman Brown 434
Office Hours: T 2:15 PM -- 3:30 PM and by appointment